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Degeneracy In Optimization Problems
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Book Synopsis Quantitative Techniques by : P. C. Tulsian
Download or read book Quantitative Techniques written by P. C. Tulsian and published by Pearson Education India. This book was released on 2006 with total page 806 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantitative Techniques: Theory and Problems adopts a fresh and novel approach to the study of quantitative techniques, and provides a comprehensive coverage of the subject. Essentially designed for extensive practice and self-study, this book will serve as a tutor at home. Chapters contain theory in brief, numerous solved examples and exercises with exhibits and tables.
Book Synopsis Optimality Conditions: Abnormal and Degenerate Problems by : Aram Arutyunov
Download or read book Optimality Conditions: Abnormal and Degenerate Problems written by Aram Arutyunov and published by Springer Science & Business Media. This book was released on 2000-10-31 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to one of the main questions of the theory of extremal problems, namely, to necessary and sufficient extremality conditions. The book consists of four parts. First, the abstract minimization problem with constraints is studied. The next chapter is devoted to one of the most important classes of extremal problems, the optimal control problem. Next, one of the main objects of the calculus of variations is studied, the integral quadratic form. Finally, local properties of smooth nonlinear mappings in a neighborhood of an abnormal point will be discussed. Audience: The book is intended for researchers interested in optimization problems. The book may also be useful for advanced students and postgraduate students.
Book Synopsis Newton-Type Methods for Optimization and Variational Problems by : Alexey F. Izmailov
Download or read book Newton-Type Methods for Optimization and Variational Problems written by Alexey F. Izmailov and published by Springer. This book was released on 2014-07-08 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will be useful to researchers and graduate students in the fields of optimization and variational analysis.
Book Synopsis Complexity In Numerical Optimization by : Panos M Pardalos
Download or read book Complexity In Numerical Optimization written by Panos M Pardalos and published by World Scientific. This book was released on 1993-07-31 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational complexity, originated from the interactions between computer science and numerical optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic difficulty.The main focus of complexity is the study of whether existing algorithms are efficient for the solution of problems, and which problems are likely to be tractable.The quest for developing efficient algorithms leads also to elegant general approaches for solving optimization problems, and reveals surprising connections among problems and their solutions.This book is a collection of articles on recent complexity developments in numerical optimization. The topics covered include complexity of approximation algorithms, new polynomial time algorithms for convex quadratic minimization, interior point algorithms, complexity issues regarding test generation of NP-hard problems, complexity of scheduling problems, min-max, fractional combinatorial optimization, fixed point computations and network flow problems.The collection of articles provide a broad spectrum of the direction in which research is going and help to elucidate the nature of computational complexity in optimization. The book will be a valuable source of information to faculty, students and researchers in numerical optimization and related areas.
Author :Christodoulos A. Floudas Publisher :Springer Science & Business Media ISBN 13 :0387747583 Total Pages :4646 pages Book Rating :4.3/5 (877 download)
Book Synopsis Encyclopedia of Optimization by : Christodoulos A. Floudas
Download or read book Encyclopedia of Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2008-09-04 with total page 4646 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
Book Synopsis System Modeling and Optimization by : F. Ceragioli
Download or read book System Modeling and Optimization written by F. Ceragioli and published by Springer Science & Business Media. This book was released on 2006-03-27 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents selected proceedings from the 22nd biennial IFIP conference on System Modeling and Optimization, held in Turin, Italy in July of 2005. This edition of the conference is dedicated to the achievements of Camillo Possio, who was killed sixty years ago during the last air raid over Turin. For more information about the 300 other books in the IFIP series, please visit www.springeronline.com.
Book Synopsis Encyclopedia of Operations Research and Management Science by : Saul I. Gass
Download or read book Encyclopedia of Operations Research and Management Science written by Saul I. Gass and published by Springer Science & Business Media. This book was released on 2001 with total page 969 pages. Available in PDF, EPUB and Kindle. Book excerpt: Audience: Anyone concerned with the science, techniques and ideas of how decisions are made."--BOOK JACKET.
Book Synopsis Optimality Conditions: Abnormal and Degenerate Problems by : A.V. Arutyunov
Download or read book Optimality Conditions: Abnormal and Degenerate Problems written by A.V. Arutyunov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to one of the main questions of the theory of extremal prob lems, namely, to necessary and sufficient extremality conditions. It is intended mostly for mathematicians and also for all those who are interested in optimiza tion problems. The book may be useful for advanced students, post-graduated students, and researchers. The book consists of four chapters. In Chap. 1 we study the abstract minimization problem with constraints, which is often called the mathemati cal programming problem. Chapter 2 is devoted to one of the most important classes of extremal problems, the optimal control problem. In the third chapter we study one of the main objects of the calculus of variations, the integral quadratic form. In the concluding, fourth, chapter we study local properties of smooth nonlinear mappings in a neighborhood of an abnormal point. The problems which are studied in this book (of course, in addition to their extremal nature) are united by our main interest being in the study of the so called abnormal or degenerate problems. This is the main distinction of the present book from a large number of books devoted to theory of extremal problems, among which there are many excellent textbooks, and books such as, e.g., [13, 38, 59, 78, 82, 86, 101, 112, 119], to mention a few.
Book Synopsis Optimization Problems by : L. Collatz
Download or read book Optimization Problems written by L. Collatz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The German edition of this book, first published in 1966, has been quite popular; we did not, however, consider publishing an English edition because a number of excellent textbooks in this field already exist. In recent years, how ever, the wish was frequently expressed that, especially, the description of the relationships between optimization and other subfields of mathematics, which is not to be found in this form in other texts, might be made available to a wider readership; so it was with this in mind that, be latedly, a translation was undertaken after all. Since the appearance of the German edition, the field of optimization has continued to develop at an unabated rate. A completely current presentation would have required a total reworking of the book; unfortunately, this was not possible. For example, we had to ignore the extensive progress which has been made in the development of numerical methods which do not require convexity assumptions to find local maxima and minima of non-linear optimization problems. These methods are also applicable to boundary value, and other, problems. Many new results, both of a numerical and a theoretical na ture, which are especially relevant to applications, are to be found in the areas of optimal contol and integer optimiza tion.
Book Synopsis Degeneracy Graphs and the Neighbourhood Problem by : H.-J. Kruse
Download or read book Degeneracy Graphs and the Neighbourhood Problem written by H.-J. Kruse and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: A few years ago nobody would have anticipated that in connection with degeneracy in Linear Programming quite a new field. could originate. In 1976 a very simple question has been posed: in the case an extreme pOint (EP) of a polytope is degenerate and the task is to find all neighbouring EP's of the degenerate EP, is it necessary to determine all basic solutions of the corresponding equalities system associated with the degenerate EP -in order to be certain to determine all neighbours of this EP? This question implied another one: Does there exists a subset of the mentioned set of basic solutions such that it suffices to find such a subset in order to determine all neighbours? The first step to solve these questions (which are motivated in the first Chapter of this book) was to define a graph (called degeneracy graph) the nodes of which correspond to the basic solutions. It turned out that such a graph has some special properties and in order to solve the above questions firstly these properties had to be investigated. Also the structure of degeneracy graphs playes hereby an important role. Because the theory of degeneracy graphs was quite new, it was necessary to elaborate first a completely new terminology and to define new notions. Dr.
Book Synopsis New Optimization Algorithms in Physics by : Alexander K. Hartmann
Download or read book New Optimization Algorithms in Physics written by Alexander K. Hartmann and published by John Wiley & Sons. This book was released on 2006-03-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many physicists are not aware of the fact that they can solve their problems by applying optimization algorithms. Since the number of such algorithms is steadily increasing, many new algorithms have not been presented comprehensively until now. This presentation of recently developed algorithms applied in physics, including demonstrations of how they work and related results, aims to encourage their application, and as such the algorithms selected cover concepts and methods from statistical physics to optimization problems emerging in theoretical computer science.
Book Synopsis Degeneracy Graphs and Simplex Cycling by : Peter Zörnig
Download or read book Degeneracy Graphs and Simplex Cycling written by Peter Zörnig and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in economics can be formulated as linearly constrained mathematical optimization problems, where the feasible solution set X represents a convex polyhedral set. In practice, the set X frequently contains degenerate verti- ces, yielding diverse problems in the determination of an optimal solution as well as in postoptimal analysis.The so- called degeneracy graphs represent a useful tool for des- cribing and solving degeneracy problems. The study of dege- neracy graphs opens a new field of research with many theo- retical aspects and practical applications. The present pu- blication pursues two aims. On the one hand the theory of degeneracy graphs is developed generally, which will serve as a basis for further applications. On the other hand dege- neracy graphs will be used to explain simplex cycling, i.e. necessary and sufficient conditions for cycling will be de- rived.
Book Synopsis Linear Programming by : Robert J Vanderbei
Download or read book Linear Programming written by Robert J Vanderbei and published by Springer Science & Business Media. This book was released on 2013-07-16 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Fourth Edition introduces the latest theory and applications in optimization. It emphasizes constrained optimization, beginning with a substantial treatment of linear programming and then proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Readers will discover a host of practical business applications as well as non-business applications. Topics are clearly developed with many numerical examples worked out in detail. Specific examples and concrete algorithms precede more abstract topics. With its focus on solving practical problems, the book features free C programs to implement the major algorithms covered, including the two-phase simplex method, primal-dual simplex method, path-following interior-point method, and homogeneous self-dual methods. In addition, the author provides online JAVA applets that illustrate various pivot rules and variants of the simplex method, both for linear programming and for network flows. These C programs and JAVA tools can be found on the book's website. The website also includes new online instructional tools and exercises.
Book Synopsis Multi-level Mixed-Integer Optimization by : Styliani Avraamidou
Download or read book Multi-level Mixed-Integer Optimization written by Styliani Avraamidou and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-06-06 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the fundamental underlying mathematical theory, numerical algorithms and effi cient computational tools for the solution of multi-level mixedinteger optimization problems. It can enable a vast array of decision makers and engineers (e.g. process engineers, bioengineers, chemical and civil engineers, and economists) to model, formulate and solve hierarchical decision making problems. The book gives detailed insights on multi-level optimization by comprehensive explanations, step-by-step numerical examples and case studies, plots, and diagrams.
Book Synopsis Mathematical Optimization and Economic Theory by : Michael D. Intriligator
Download or read book Mathematical Optimization and Economic Theory written by Michael D. Intriligator and published by SIAM. This book was released on 2002-01-01 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic account of mathematical programming and control techniques and their applications to static and dynamic problems in economics.
Book Synopsis Optimization Methods in Finance by : Gerard Cornuejols
Download or read book Optimization Methods in Finance written by Gerard Cornuejols and published by Cambridge University Press. This book was released on 2006-12-21 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses.
Book Synopsis Optimization and Applications by : Nicholas Olenev
Download or read book Optimization and Applications written by Nicholas Olenev and published by Springer Nature. This book was released on 2023-01-02 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th International Conference on Optimization and Applications, OPTIMA 2022, held in Petrovac, Montenegro, during September 26–30, 2022. The 17 full papers and presented were carefully reviewed and selected from 43 submissions. They were organized into the following as follows: mathematical programming; global optimization; discrete and combinatorial optimization; optimal control; optimization and data analysis; and game theory and mathematical economics.
